Transient Heat Transfer Analysis of Functionally Graded Composite Plates by Richardson Extrapolation Based Reduced Integration Scheme

The objective of the studies presented in this paper is the numerical prediction of unsteady heat flux and pressure fluctuations during the unstable regime of a combustor. The studied laboratory-scale lean partially premixed combustor was built in the LIMOUSINE project, to explore the mechanisms driving thermo-acoustic instabilities in conditions representative of gas turbine combustors. Due to the thermal interaction between hot gases and the colder liner wall, and also the correlation between gas temperature, density and speed of sound, prediction of the transient heat transfer rate is of high importance. In this paper analysis of transient heat transfer is conducted by coupling of fluid flow and solid body (liner) in one computational domain and thereby taking into account the thermal convection with the environment around the combustor and also the heat conduction transients within the liner. Conjugate heat transfer modeling can give access to the transient temperature distribution in the structure of the combustor which is important for the dynamic heat storage. Also this can be used to estimate the thermal stresses and creep strain as required to evaluate the lifetime assessment of the combustor. In this work the commercial CFD code ANSYS CFX is used to solve the problem, in which fluid and solid regions are solved simultaneously with a finite volume approach. In the fluid region, three dimensional compressible Reynolds Averaged Navier-Stokes equations are solved, while for the solid region only the enthalpy conservation equation is solved. To remove any interpolation errors, in all cases the skin (interface) mesh cells for both the fluid and solid are similar in resolution on either side of the interface. By comparing heat release and pressure data available from the measurements it follows that this simulation can give more accurate prediction of the amplitudes of thermoacoustic instabilities as compared to the solution with imposed thermal boundary conditions (such as isothermal). In the latter case the time history of heat accumulation in the solid is predicted incorrectly. Because the spatial scales of the solid temperature profiles are different in case of steady state or transient oscillatory heat transfer, care has to be taken in the meshing in these two situations. When meshing for a transient oscillatory heat transfer case, the solid mesh resolution needs to be adapted to the thermal penetration depth of the surface temperature oscillations. Hence for the transient heat transfer in limit cycle combustion oscillations, the meshing strategy and size of the grid in the solid part of the domain will play a very important role in determining the magnitude for the pressure fluctuations.

The objectives of this study are (i) to find exact analytical solutions to the unsteady hybrid nanofluid flow and heat transfer due to a moving infinite flat plate, and (ii) to investigate the impacts of different hybrid nanofluids (Cu‐Al2O3/water, CuO‐Al2O3/water, and Ag‐Al2O3/water) on the unsteady flow and heat transfer characteristics with MHD and variable temperature. The Laplace transform technique is employed to find the exact analytical solutions of the partial differential equations with appropriate boundary conditions governing the problem considered. The results computed for engineering quantities, namely skin friction coefficient and Nusselt number and velocity and temperature profiles by the Laplace transform technique are analyzed using graphs and tables. It has been found that there is a significant increase in the heat transfer rate for hybrid nanofluids than for nanofluids and we observed a higher heat transfer rate for Cu‐Al2O3/water and a lower heat transfer rate for Ag‐Al2O3/water than for the others. The novelty of this study is finding an exact analytical solution to the problem of hybrid nanofluid flow due to moving vertical plate where the effects of magnetic field and variable plate temperature conditions are considered. The obtained results can be used in various engineering applications, including geothermal reservoirs, packed‐bed storage tanks, packed‐bed catalytic reactors, thermal insulation, grain storage, porous solids drying, and petroleum resource gas production. Furthermore, the findings can be used to validate numerical solutions for more complex transient hybrid nanofluid flow and convective heat transfer problems.

This paper discusses the problem of heat transfer in service based on unsteady heat transfer theory. Firstly, the unsteady partial differential heat transfer equations are established according to the law of conservation of energy, and the initial values and boundary conditions are determined. Two unknown convective heat transfer coefficients are involved in the heat transfer model of the work suit. The optimal heat transfer coefficient is determined by describing the numerical relationship and solving the optimization problem, which can be applied to the thickness design of the work suit. The relationship between the convective heat transfer coefficient and the measured temperature is established by the least square method. Furthermore, the unsteady heat transfer model is solved numerically by explicit difference method, and the stability and accuracy of the model are verified. Finally, according to the solution results, the temperature distribution and parameter fitting effect of the work suit are shown, which proves the effectiveness and reliability of the model in practical application.

Numerical investigation of transport phenomena properties on transient heat transfer in a vertical pipe flow

The effect of the upstream wake on the time averaged rotor blade heat transfer was numerically investigated. The geometry and flow conditions of the first stage turbine blade of GE’s E3 engine with a tip clearance equal to 2% of the span were utilized. The upstream wake had both a total pressure and temperature deficit. The rotor inlet conditions were determined from a steady analysis of the cooled upstream vane. Comparisons between the time average of the unsteady rotor blade heat transfer and the steady analysis, which used the average inlet conditions of unsteady cases, are made to illuminate the differences between the steady and unsteady calculations. To help in the understanding of the differences between steady and unsteady results on one hand and to evaluate the effect of the total temperature wake on the other, separate calculations were performed to obtain the rotor heat transfer and adiabatic wall temperatures. It was found that the Nusselt number distribution for the time average of unsteady heat transfer is invariant if normalized by the difference in the adiabatic and wall temperatures. It appeared though that near the endwalls the Nusselt number distribution did depend on the thermal wake strength. Differences between steady and time averaged unsteady heat transfer results of up to 20% were seen on the blade surface. Differences were less on the blade tip surface.

Local/global analysis of transient heat transfer from building foundations

Unsteady Convective Heat Transfer and Hydrodynamics in Channels

This paper investigates a novel meshfree approach for transient heat transfer analysis of isotropic material using the Interpolating Moving Least Squares (IMLS). Building upon the strengths of meshless methods, particularly the Element-Free Galerkin (EFG) approach, the proposed method leverages the IMLS technique to construct shape functions that satisfy the Kronecker delta property, thereby allowing essential boundary conditions to be imposed directly without additional transformation or penalty methods. This significantly simplifies the numerical implementation while maintaining the flexibility and adaptability of meshfree formulations. The IMLS-based scheme is integrated within the Galerkin weak form framework to develop a robust and accurate numerical model capable of simulating transient heat transfer behavior. Unlike traditional finite element methods (FEM), which often require complex meshing procedures and suffer from accuracy issues in problems with evolving geometries of sharp gradients, the proposed meshfree method offers enhanced computational precision and geometric flexibility. The implementation is carried out in MATLAB. First, to evaluate the performance and reliability of the method, a convergence study is conducted using various nodal distributions. This analysis identified suitable node densities and support domain sizes that yield optimal accuracy and computational efficiency. The present results are then validated and verified through comparison with benchmark problems and previously published results. The numerical results demonstrate excellent agreement with the reference results, confirming the precision of the proposed IMLS-based approach. Following the validation phase, a detailed parameter sensitivity analysis was performed to investigate the influence of parameters on the temperature distribution of the structure. Finally, the method is applied to a transient heat transfer problem in a complex-shaped isotropic domain to assess its capability to handle real-world engineering problems. These findings establish a valuable benchmark for the ongoing advancement of meshfree methods and provide a solid foundation for future investigations into the applicability of methods to complex and practical engineering problems.

The research described in this paper is a numerical investigation of the effects of unsteady flow on gas turbine heat transfer, particularly on a rotor blade surface. The unsteady flow in a rotor blade passage and the unsteady heat transfer on the blade surface as a result of wake/blade interaction are modeled by the inviscid flow/boundary layer approach. The Euler equations that govern the inviscid flow are solved using a time-accurate marching scheme. The unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. Unsteady flow solutions in the passage provide pressure gradients and boundary conditions for the boundary-layer equations that govern the viscous flow adjacent to the blade surface. Numerical solutions of the unsteady turbulent boundary layer yield surface heat flux values that can then be compared to experimental data. Comparisons with experimental data show that unsteady heat flux on the blade suction surface is well predicted, but the predictions of unsteady heat flux on the blade pressure surface do not agree.

The research described in this paper is a numerical investigation of the effects of unsteady flow on gas turbine heat transfer, particularly on a rotor blade surface. The unsteady flow in a rotor blade passage and the unsteady heat transfer on the blade surface as a result of wake/blade interaction are modeled by the inviscid flow/boundary layer approach. The Euler equations which govern the inviscid flow are solved using a time accurate marching scheme. The unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. Unsteady flow solutions in the passage provide pressure gradients and boundary conditions for the boundary-layer equations which govern the viscous flow adjacent to the blade surface. Numerical solutions of the unsteady turbulent boundary layer yield surface heat flux values which can then be compared to experimental data. Comparisons with experimental data show that unsteady heat flux on the blade suction surface is well predicted, but the predictions of unsteady heat flux on the blade pressure surface do not agree.

Transient heat and mass transfer in the two-phase system: Subliming solid-vapour-gas mixture

Friction stir welding (FSW) is a favorable welding technology for aluminum alloys. The FSW process involves complex heat and mass transfer. Explicit meshless particle methods are currently popular methods for simulating the process, but they require expensive computational cost. Coupling explicit finite element method (FEM) and meshless particle methods can ease the problem by making use of high efficiency of FEM and advantages of meshless particle methods. Though many efforts have been made to couple FEM and meshless particle methods for transient dynamics problems, coupling them for transient heat transfer problems is seldom addressed. In this work, we focus on treating this problem. We developed an explicit coupled method of FEM and the meshless particle method presented in a previous work and used it to simulate the thermal process during FSW. In the method, FEM using lumped heat capacity matrix and low-order numerical integration is constructed to obtain high efficiency. A new coupling algorithm is proposed to link thermal calculations of the weak-form FEM and the strong-form meshless particle method. Forward Euler method is used for time integration to achieve an explicit algorithm. The coupled method is used to calculate a numerical example having analytical solution. Calculated results show that it can achieve a good accuracy. The method is employed to simulate FSW of Al 6061-T6 plates. It predicts thermal cycles in good agreement with experimental results. It shows an accuracy comparable to that of the meshless particle method while having a higher efficiency than the latter.

Unsteady flow and heat transfer on an accelerating surface with blowing or suction in the absence and presence of a heat source or sink

NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract Development and Implementation of Interactive/Visual Software for Steady State and Transient Heat Conduction Problems Afshin J. Ghajar, Ronald D. Delahoussaye, Hassouneh Al-Matar School of Mechanical and Aerospace Engineering, Oklahoma State University Stillwater, OK 74078 ghajar@ceat.okstate.edu Abstract This paper describes a versatile, user-friendly, and easy to understand computer program that has been developed to teach the numerical solution of steady state and transient heat conduction. The program has been class room tested for many semesters and it was very well received by the students. Introduction The school of Mechanical and Aerospace Engineering at Oklahoma State University offers MAE 3233, “Heat Transfer”, as a required course for the Mechanical Engineering degree and an elective course for the Aerospace Engineering degree. Student use of software to analyze 1-D and 2-D steady state and transient heat conduction problems has been an important part of this course since 1994. Use of software has been particularly important in appreciating the power of numerical methods in solving engineering heat transfer problems. The software described in this paper is based on the finite difference method and can handle three types of boundary conditions (constant temperature, specified heat flux, and convection) and two types of numerical schemes (implicit and explicit). The user has access to a built in material properties library for selection of realistic material properties. The program provides tabular output, graphical output, and shaded and animated temperature plots for steady and transient cases. The primary goal of this project was to develop MS Windows based software that is effective for teaching; easy to use, maintain and update; and freely available to all. Motivation for the Project Before starting this project, the authors were aware of many existing software options for computer based heat transfer analysis. Unfortunately, all of them had major drawbacks for our purposes. There are professional level programs that can perform highly detailed heat transfer and fluid flow analysis, and most are available at a substantial educational discount. These programs have three major drawbacks: they are not designed to teach numerical heat transfer analysis; the time required to learn to use these programs is substantial; and the cost to individual students is still fairly high. Many heat transfer textbooks (see for example References 1 and 2) now include software aimed at teaching the concepts of numerical heat transfer analysis, but these are only available to students who purchase the textbook. Our preferred textbook did not offer such software at the time we undertook this project. In general, we prefer to choose the textbook on the basis of the content of the book itself. Any software provided by the book is an added bonus. This paper is in no way intended as a criticism of the software available with current Heat Transfer textbooks. 1

A deep collocation method for heat transfer in porous media: Verification from the finite element method